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hope - these difficulties will have been cleared up? Only a
prophet or the seventh son of a prophet sticks Ms head into the
noose of prediction. But if there is any continuity at all in the
evolution of'mathematics - and the majority of dispassionate
observers believe that there is - we shall find that the mathe-
matics which is to come will be broader, firmer, and richer in
content than that which we or our predecessors have known.
Already the controversies of the past third of a century have
added new fields - including totally new logics - to the vast
domain of mathematics, and the new is being rapidly consoli-
dated and co-ordinated with^the old. If we may rashly venture
a prediction, what is to come will be fresher, younger in every
. respect, and closer to human thought and human needs - freer
of appeal for its justification to extra-human 'existences' - than
what is now being vigorously refashioned. The spirit of mathe-
matics is  eternal youth. As Cantor said, 6The essence of mathe-
matics resides in its freedom*; the present 'revolution' is but
another assertion of that freedom.